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Graph is Bipartite

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a C# program to implement the isBipartite(int[][] graph) function, which determines if a given undirected graph can be colored with exactly two colors such that no two adjacent vertices share the same color. The graph is given as an adjacency list where graph[i] contains all the neighbors of vertex i.

Example 1
    
  
  • Input: graph = [[1,3],[0,2],[1,3],[0,2]]
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  • Output: true
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  • Explanation: 
    
      
      
    • We can color vertex 0 with color 0, vertex 1 with color 1, vertex 2 with color 0, and vertex 3 with color 1.
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    • No two adjacent vertices share the same color.
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Example 2
    
  
  • Input: graph = [[1,2,3],[0,2],[0,1,3],[0,2]]
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  • Output: false
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  • Explanation: 
    
      
      
    • There is no way to color the vertices with two colors without adjacent vertices sharing the same color.
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    • For example, if vertex 0 has color 0, then vertices 1, 2, and 3 must all have color 1.
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    • But vertices 1 and 2 are adjacent, so they cannot have the same color.
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Constraints
    
  
  • 1 ≤ graph.length ≤ 100
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  • 0 ≤ graph[i].length ≤ 100
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  • graph[i] does not contain i
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  • There are no self-loops or parallel edges
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  • Time Complexity: O(V + E) where V is the number of vertices and E is the number of edges
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  • Space Complexity: O(V)
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GraphTech MahindraTutorix
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Hint
Solution

Solution Hints

    
  
  • Use either Breadth-First Search (BFS) or Depth-First Search (DFS) to traverse the graph
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  • Assign colors (e.g., 0 and 1) to vertices as you visit them
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  • If you encounter a vertex that has already been colored and its color conflicts with what it should be, the graph is not bipartite
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  • Remember to handle disconnected components of the graph
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  • Use an array to track the color of each vertex
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Steps to solve by this approach:

 Step 1: Create an array to store the color of each vertex (-1 for uncolored, 0 and 1 for the two colors).
 Step 2: For each uncolored vertex, start a BFS traversal.
 Step 3: Color the starting vertex and enqueue it.
 Step 4: For each vertex in the queue, calculate the expected color of its neighbors (opposite of the current vertex's color).
 Step 5: For each neighbor, if it's uncolored, color it with the expected color and enqueue it.
 Step 6: If a neighbor is already colored and its color doesn't match the expected color, the graph is not bipartite.
 Step 7: If all vertices can be colored without conflicts, the graph is bipartite.

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